If you've had any experience with electronics, you may be wondering why you've never heard of this "conductance" before. You may be more familiar with the resistance \(R\), the reciprocal of the conductance. $$R=\frc{G}$$ When resistance increases, conductance decreases, and the amount of current through the wire drops. The relationship between potential difference and current is given by $$\Dl V=IR$$ which is called Ohm's Law. The resistance of a wire is given by $$R=\rho \frac{L}{A}$$ where \(\rho=\frc{\sigma}\) is the resistivity of the material of the wire: glass has a high resistivity and metal has a low resisitivity.

The SI units of resistance are ohms, written as Ω: $$[R]=\left[\frac{\Dl V}{I}\right]=\frac{V}{A}=\Omega$$ The units of conductance are inverse ohms, which goes by two different names: the official SI unit is the siemens (S), but I prefer calling it the mho ℧.

All objects and devices can be said to have a resistance, not just wires: but of course \(R=\rho L/A\) doesn't work for a TV or a light bulb. In general, Ohm's Law actually defines the resistance of a device: hook up the device to a potential difference \(\Dl V\), measure the current \(I\) that flows through the device, and the resistance of the device is $$R=\frac{\Dl V}{I}$$
A typical carbon resistor

Interactive 10.4.1